Can I save rendered images as PNG with a sRGB color profile?
There is a sizable degree of erroneous information listed here; some lacking clarity, while other bits could be classified as entirely misinformation or misleading.


  Where can I set the color space of images?


Complex question that requires a deeper understanding of colour management and in particular, how OpenColorIO is designed, but the short answer is from the UV Image Viewer's Properties panel.


  Does this mean the image are saved in sRGB by default but no color
  profile is attached to the image ?


If you do nothing to the default configuration, yes.


  So best to assign sRGB to the image
  when opened in Photoshop?


Yes.


  How is Blender saving the images ... with to without color profile?


Yes.


  And is that sRGB?


Complex question, but simple answer is “Yes.”